Solve for $x$ and $y$ using elimination. $\begin{align*}-3x+6y &= 9 \\ -8x-6y &= -6\end{align*}$
Answer: We can eliminate $y$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $-11x = 3$ Divide both sides by $-11$ and reduce as necessary. $x = -\dfrac{3}{11}$ Substitute $-\dfrac{3}{11}$ for $x$ in the top equation. $-3( -\dfrac{3}{11})+6y = 9$ $\dfrac{9}{11}+6y = 9$ $6y = \dfrac{90}{11}$ $y = \dfrac{15}{11}$ The solution is $\enspace x = -\dfrac{3}{11}, \enspace y = \dfrac{15}{11}$.